Systems of Particles and Rotational Motion

Question : 2

Total: 33

In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27Å(1Å=10–10m). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

Solution:

Let C.M. be at a distance x Å from H-atom
Distance of C.M. from Cl atom =(1.27–x)Å

Let the mass of H-atom = m units
The mass of the Cl-atom = 35.5 m units
If C.M. is taken at the origin, then
mx+(1.27–x)35.5m=0
mx=–(1.27–x)35.5m
Negative sign indicatesthat if Cl atom is on the right side of C.M.(+), the hydrogen atom is on the left side of C.M. So, avoiding, if we get
x+35.5x=1.27×35.5
36.5x=45.085
x=

45.005

36.5

=1.235Å
Therefore, the centre of mass located on theline joining H and Cl nuclei at a distance of 1.24 Å from the H atom.

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